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Map (mathematics)

Function, homomorphism, or morphism / From Wikipedia, the free encyclopedia

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In mathematics, a map or mapping is a function in its general sense.[1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper.[2]

One type of map is a function, as in the association of any of the four colored shapes in X to its color in Y

The term map may be used to distinguish some special types of functions, such as homomorphisms. For example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial.[3][4] In category theory, a map may refer to a morphism.[2] The term transformation can be used interchangeably,[2] but transformation often refers to a function from a set to itself. There are also a few less common uses in logic and graph theory.